Map tile terrain transitions with 3-4 different types

Making transitions between two different tiles is a fairly well understood problem. The easiest way is to look at the 0.5, 0.5 and use the resulting 4 corner points to select a transition tile, as mentioned here for example: http://playtechs.blogspot.se/2007/04/tileset-design-tip.html

The problem comes when three or four tiles meet, for example:

(s for swamp, p for plains and . for water)

pppp

..sp
..pp

If we look at the offset in the corner, the edges in our transition tile looks like:

pp
.s

In this case there are no suitable transition tiles to be found, as they typically are created to work between 2 types only. Unless we work out a three way transition tile with these types, we appear to be stuck.

I'm well aware of this often referenced article on the tile transitions in Artifact: http://archive.gamedev.net/archive/reference/articles/article934.html

But looking at the actual screenshots from that game, it doesn't seem like it will yield professional looking maps: http://www.samugames.com/artifact/screenshots.htm

Aside from using intermediary tiles (which frankly would be problematic since two out of grassland/swamp/desert would then not be able to border directly to water), are there any solutions?

EDIT

I think I've found a solution that can will create terrain transitions for 3-4 different types, using only one extra transition tile to each set of transition tiles. I've yet to make an implementation of the algorithm, but the mockups look fine. This solution will work well for pixel art.